Optical data processing can often be used to process data more rapidly and efficiently than conventional computational methods. In particular, optical methods can be used to perform linear transformations of data sets rapidly and efficiently.
For example, it is well known that converging lenses can be used to substantially “instantaneously” transform a first image into a second image that is a Fourier transform of the first image. It is to be noted that the Fourier transform is a relationship between the complex amplitudes of light in the images and not between the intensities of light in the images. The same is generally true with respect to other transformations of images, the transformation is a transformation of complex amplitudes of light and not intensities of light. It is therefore to be understood that when a second image is said to be a Fourier, or other, transform of a first image, what is meant is that the spatial pattern of the complex amplitude of light in the second image is the Fourier, or other, transform of the spatial pattern of the complex amplitude of light in the first image.
If the first image is coded with data, the second image is coded with data that is the Fourier transform of the data in the first image. A suitable optical processor can therefore provide substantial advantages in comparison to a conventional data processor when a spectral analysis of a data set is desired. However, a Fourier transform of a data set in general involves complex numbers, even if the data set comprises only real numbers. Therefore, in order to properly detect an “optical” Fourier transform of a data set, phase as well as intensity of light of an image representing the Fourier transform must be detected. While this can be accomplished, most light detectors are generally sensitive only to light intensity and are not responsive to phase.
It is therefore generally more convenient to determine values for data represented by an image from only the intensity of light in the image. Consequently, it is usually advantageous to process data optically using methods that generate only real numbers from the data.
For example, it is often preferable to optically process data coded in an image in accordance with a cosine transform to perform a spectral analysis of the data rather than a Fourier transform. The cosine transform of a real data set generates real values. However, whereas a cosine transform of a real data set does not generate complex numbers it does, usually, generate both positive and negative numbers. Therefore, while most of the information in an optical cosine transform of an image can be acquired from measurements of intensity of light in the image, sign information is not preserved in the intensity measurements. As a result, an optical processor that transforms an input image into an output image that represents the cosine transform of the input image requires a means for determining which of the numbers represented by the output image are positive and which are negative.
K. W. Wong et al, in an article entitled “Optical cosine transform using microlens array and phase-conjugate mirror ”, Jpn J. Appl. Phys. vol. 31, 1672-1676, the disclosure of which is incorporated herein by reference, describes a method of distinguishing positive and negative data in a cosine transform of an image.
The problem of distinguishing the sign of numbers represented by an image when only the intensity of light in the image is measured is of course not limited to the case of data optically generated by a cosine transform. The problem affects all real linear transforms, such as for example the sine and discrete sine transforms and the Hartley transform, when the transforms are executed optically and only their intensities are sensed, if they generate both positive and negative values from a real data set.